Paper - Regressie analyse 1

*The author of this computation has been verified*

R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Sun, 28 Nov 2010 20:06:50 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Nov/28/t1290974723acxsfsaze6mqdpq.htm/, Retrieved Sun, 28 Nov 2010 21:05:33 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Nov/28/t1290974723acxsfsaze6mqdpq.htm/}, year = {2010}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2010}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

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User-defined keywords:

Dataseries X:

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376.974 377.632 378.205 370.861 369.167 371.551 382.842 381.903 384.502 392.058 384.359 388.884 386.586 387.495 385.705 378.67 377.367 376.911 389.827 387.82 387.267 380.575 372.402 376.74 377.795 376.126 370.804 367.98 367.866 366.121 379.421 378.519 372.423 355.072 344.693 342.892 344.178 337.606 327.103 323.953 316.532 306.307 327.225 329.573 313.761 307.836 300.074 304.198 306.122 300.414 292.133 290.616 280.244 285.179 305.486 305.957 293.886 289.441 288.776 299.149 306.532 309.914 313.468 314.901 309.16 316.15 336.544 339.196 326.738 320.838 318.62 331.533 335.378

Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits! Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 6 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Maandelijksewerkloosheid[t] = + 340.566 + 7.08614285714269M1[t] + 7.6318333333334M2[t] + 4.00366666666672M3[t] + 0.597500000000047M4[t] -3.84333333333325M5[t] -3.52949999999995M6[t] + 12.9915000000001M7[t] + 13.2620000000001M8[t] + 5.86350000000007M9[t] + 0.404000000000063M10[t] -5.74533333333328M11[t] + e[t] Multiple Linear Regression - Ordinary Least Squares Variable Parameter S.D. T-STAT H0: parameter = 0 2-tail p-value 1-tail p-value (Intercept) 340.566 15.36219 22.1691 0 0 M1 7.08614285714269 20.935136 0.3385 0.736163 0.368082 M2 7.6318333333334 21.725418 0.3513 0.726584 0.363292 M3 4.00366666666672 21.725418 0.1843 0.854401 0.427201 M4 0.597500000000047 21.725418 0.0275 0.978149 0.489074 M5 -3.84333333333325 21.725418 -0.1769 0.860169 0.430085 M6 -3.52949999999995 21.725418 -0.1625 0.871481 0.435741 M7 12.9915000000001 21.725418 0.598 0.552063 0.276031 M8 13.2620000000001 21.725418 0.6104 0.54384 0.27192 M9 5.86350000000007 21.725418 0.2699 0.788155 0.394077 M10 0.404000000000063 21.725418 0.0186 0.985224 0.492612 M11 -5.74533333333328 21.725418 -0.2645 0.792323 0.396162 Multiple Linear Regression - Regression Statistics Multiple R 0.172553432785642 R-squared 0.029774687166109 Adjusted R-squared -0.145183975803937 F-TEST (value) 0.170181268310256 F-TEST (DF numerator) 11 F-TEST (DF denominator) 61 p-value 0.998574183030723 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 37.6295272027582 Sum Squared Residuals 86374.8603676904 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 376.974 347.652142857144 29.3218571428557 2 377.632 348.197833333333 29.4341666666666 3 378.205 344.569666666667 33.6353333333333 4 370.861 341.1635 29.6975000000000 5 369.167 336.722666666667 32.4443333333333 6 371.551 337.0365 34.5145 7 382.842 353.5575 29.2845 8 381.903 353.828 28.075 9 384.502 346.4295 38.0725 10 392.058 340.97 51.088 11 384.359 334.820666666667 49.5383333333333 12 388.884 340.566 48.3180000000001 13 386.586 347.652142857143 38.9338571428574 14 387.495 348.197833333333 39.2971666666667 15 385.705 344.569666666667 41.1353333333333 16 378.67 341.1635 37.5065 17 377.367 336.722666666667 40.6443333333333 18 376.911 337.0365 39.8745 19 389.827 353.5575 36.2695 20 387.82 353.828 33.992 21 387.267 346.4295 40.8375 22 380.575 340.97 39.605 23 372.402 334.820666666667 37.5813333333333 24 376.74 340.566 36.1740000000001 25 377.795 347.652142857143 30.1428571428574 26 376.126 348.197833333333 27.9281666666667 27 370.804 344.569666666667 26.2343333333333 28 367.98 341.1635 26.8165 29 367.866 336.722666666667 31.1433333333333 30 366.121 337.0365 29.0845 31 379.421 353.5575 25.8635 32 378.519 353.828 24.691 33 372.423 346.4295 25.9935 34 355.072 340.97 14.102 35 344.693 334.820666666667 9.87233333333331 36 342.892 340.566 2.32600000000005 37 344.178 347.652142857143 -3.47414285714262 38 337.606 348.197833333333 -10.5918333333333 39 327.103 344.569666666667 -17.4666666666666 40 323.953 341.1635 -17.2105000000000 41 316.532 336.722666666667 -20.1906666666667 42 306.307 337.0365 -30.7295000000000 43 327.225 353.5575 -26.3325 44 329.573 353.828 -24.2550000000000 45 313.761 346.4295 -32.6685 46 307.836 340.97 -33.134 47 300.074 334.820666666667 -34.7466666666667 48 304.198 340.566 -36.3680 49 306.122 347.652142857143 -41.5301428571426 50 300.414 348.197833333333 -47.7838333333333 51 292.133 344.569666666667 -52.4366666666667 52 290.616 341.1635 -50.5475 53 280.244 336.722666666667 -56.4786666666666 54 285.179 337.0365 -51.8575 55 305.486 353.5575 -48.0715 56 305.957 353.828 -47.871 57 293.886 346.4295 -52.5435 58 289.441 340.97 -51.529 59 288.776 334.820666666667 -46.0446666666666 60 299.149 340.566 -41.4169999999999 61 306.532 347.652142857143 -41.1201428571426 62 309.914 348.197833333333 -38.2838333333333 63 313.468 344.569666666667 -31.1016666666666 64 314.901 341.1635 -26.2625 65 309.16 336.722666666667 -27.5626666666667 66 316.15 337.0365 -20.8865 67 336.544 353.5575 -17.0135000000000 68 339.196 353.828 -14.6320000000000 69 326.738 346.4295 -19.6915 70 320.838 340.97 -20.1320000000000 71 318.62 334.820666666667 -16.2006666666667 72 331.533 340.566 -9.03299999999992 73 335.378 347.652142857143 -12.2741428571426 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 15 0.00779846076505827 0.0155969215301165 0.992201539234942 16 0.00186247244708416 0.00372494489416833 0.998137527552916 17 0.000498485719017094 0.000996971438034188 0.999501514280983 18 0.000108356068943110 0.000216712137886221 0.999891643931057 19 2.74507807691628e-05 5.49015615383256e-05 0.99997254921923 20 6.37998528405823e-06 1.27599705681165e-05 0.999993620014716 21 1.32972236698331e-06 2.65944473396662e-06 0.999998670277633 22 8.59955654511575e-07 1.71991130902315e-06 0.999999140044346 23 5.92412625450168e-07 1.18482525090034e-06 0.999999407587375 24 4.21462116978146e-07 8.42924233956291e-07 0.999999578537883 25 1.38218526606853e-07 2.76437053213705e-07 0.999999861781473 26 6.58979633211423e-08 1.31795926642285e-07 0.999999934102037 27 7.18183666998822e-08 1.43636733399764e-07 0.999999928181633 28 4.43421951515017e-08 8.86843903030035e-08 0.999999955657805 29 3.58429839086521e-08 7.16859678173043e-08 0.999999964157016 30 4.74078888619272e-08 9.48157777238544e-08 0.999999952592111 31 5.32344907582851e-08 1.06468981516570e-07 0.99999994676551 32 6.46585054750482e-08 1.29317010950096e-07 0.999999935341495 33 5.00289609891879e-07 1.00057921978376e-06 0.99999949971039 34 9.78723606968299e-05 0.000195744721393660 0.999902127639303 35 0.0028676443430122 0.0057352886860244 0.997132355656988 36 0.0299483783335958 0.0598967566671916 0.970051621666404 37 0.101602305619611 0.203204611239222 0.89839769438039 38 0.293019114300803 0.586038228601606 0.706980885699197 39 0.552686969963113 0.894626060073774 0.447313030036887 40 0.709783943828292 0.580432112343417 0.290216056171708 41 0.838523562470013 0.322952875059974 0.161476437529987 42 0.908971031795041 0.182057936409918 0.0910289682049588 43 0.927835163483651 0.144329673032698 0.0721648365163492 44 0.933073128364145 0.13385374327171 0.066926871635855 45 0.946699860866973 0.106600278266055 0.0533001391330275 46 0.952183843640513 0.0956323127189742 0.0478161563594871 47 0.95190084821779 0.0961983035644201 0.0480991517822101 48 0.94931865290646 0.101362694187078 0.050681347093539 49 0.946697245320135 0.106605509359730 0.0533027546798649 50 0.93812007156245 0.123759856875100 0.0618799284375499 51 0.93470498353978 0.130590032920441 0.0652950164602207 52 0.927613876028725 0.14477224794255 0.072386123971275 53 0.925506740873205 0.148986518253589 0.0744932591267947 54 0.918470024845228 0.163059950309544 0.0815299751547722 55 0.904429835766573 0.191140328466855 0.0955701642334274 56 0.889251422891438 0.221497154217125 0.110748577108562 57 0.867977443127807 0.264045113744386 0.132022556872193 58 0.827061397972247 0.345877204055506 0.172938602027753 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 20 0.454545454545455 NOK 5% type I error level 21 0.477272727272727 NOK 10% type I error level 24 0.545454545454545 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

R code (references can be found in the software module):

library(lattice) library(lmtest) n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test par1 <- as.numeric(par1) x <- t(y) k <- length(x[1,]) n <- length(x[,1]) x1 <- cbind(x[,par1], x[,1:k!=par1]) mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1]) colnames(x1) <- mycolnames #colnames(x)[par1] x <- x1 if (par3 == 'First Differences'){ x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep=''))) for (i in 1:n-1) { for (j in 1:k) { x2[i,j] <- x[i+1,j] - x[i,j] } } x <- x2 } if (par2 == 'Include Monthly Dummies'){ x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep =''))) for (i in 1:11){ x2[seq(i,n,12),i] <- 1 } x <- cbind(x, x2) } if (par2 == 'Include Quarterly Dummies'){ x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep =''))) for (i in 1:3){ x2[seq(i,n,4),i] <- 1 } x <- cbind(x, x2) } k <- length(x[1,]) if (par3 == 'Linear Trend'){ x <- cbind(x, c(1:n)) colnames(x)[k+1] <- 't' } x k <- length(x[1,]) df <- as.data.frame(x) (mylm <- lm(df)) (mysum <- summary(mylm)) if (n > n25) { kp3 <- k + 3 nmkm3 <- n - k - 3 gqarr <- array(NA, dim=c(nmkm3-kp3+1,3)) numgqtests <- 0 numsignificant1 <- 0 numsignificant5 <- 0 numsignificant10 <- 0 for (mypoint in kp3:nmkm3) { j <- 0 numgqtests <- numgqtests + 1 for (myalt in c('greater', 'two.sided', 'less')) { j <- j + 1 gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value } if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1 if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1 if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1 } gqarr } bitmap(file='test0.png') plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index') points(x[,1]-mysum$resid) grid() dev.off() bitmap(file='test1.png') plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index') grid() dev.off() bitmap(file='test2.png') hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals') grid() dev.off() bitmap(file='test3.png') densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals') dev.off() bitmap(file='test4.png') qqnorm(mysum$resid, main='Residual Normal Q-Q Plot') qqline(mysum$resid) grid() dev.off() (myerror <- as.ts(mysum$resid)) bitmap(file='test5.png') dum <- cbind(lag(myerror,k=1),myerror) dum dum1 <- dum[2:length(myerror),] dum1 z <- as.data.frame(dum1) z plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals') lines(lowess(z)) abline(lm(z)) grid() dev.off() bitmap(file='test6.png') acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function') grid() dev.off() bitmap(file='test7.png') pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function') grid() dev.off() bitmap(file='test8.png') opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0)) plot(mylm, las = 1, sub='Residual Diagnostics') par(opar) dev.off() if (n > n25) { bitmap(file='test9.png') plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint') grid() dev.off() } load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE) a<-table.row.end(a) myeq <- colnames(x)[1] myeq <- paste(myeq, '[t] = ', sep='') for (i in 1:k){ if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '') myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ') if (rownames(mysum$coefficients)[i] != '(Intercept)') { myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='') if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='') } } myeq <- paste(myeq, ' + e[t]') a<-table.row.start(a) a<-table.element(a, myeq) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable1.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Variable',header=TRUE) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'S.D.',header=TRUE) a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE) a<-table.element(a,'2-tail p-value',header=TRUE) a<-table.element(a,'1-tail p-value',header=TRUE) a<-table.row.end(a) for (i in 1:k){ a<-table.row.start(a) a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE) a<-table.element(a,mysum$coefficients[i,1]) a<-table.element(a, round(mysum$coefficients[i,2],6)) a<-table.element(a, round(mysum$coefficients[i,3],4)) a<-table.element(a, round(mysum$coefficients[i,4],6)) a<-table.element(a, round(mysum$coefficients[i,4]/2,6)) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable2.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple R',1,TRUE) a<-table.element(a, sqrt(mysum$r.squared)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'R-squared',1,TRUE) a<-table.element(a, mysum$r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Adjusted R-squared',1,TRUE) a<-table.element(a, mysum$adj.r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (value)',1,TRUE) a<-table.element(a, mysum$fstatistic[1]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE) a<-table.element(a, mysum$fstatistic[2]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE) a<-table.element(a, mysum$fstatistic[3]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'p-value',1,TRUE) a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3])) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Residual Standard Deviation',1,TRUE) a<-table.element(a, mysum$sigma) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Sum Squared Residuals',1,TRUE) a<-table.element(a, sum(myerror*myerror)) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable3.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Time or Index', 1, TRUE) a<-table.element(a, 'Actuals', 1, TRUE) a<-table.element(a, 'Interpolation<br />Forecast', 1, TRUE) a<-table.element(a, 'Residuals<br />Prediction Error', 1, TRUE) a<-table.row.end(a) for (i in 1:n) { a<-table.row.start(a) a<-table.element(a,i, 1, TRUE) a<-table.element(a,x[i]) a<-table.element(a,x[i]-mysum$resid[i]) a<-table.element(a,mysum$resid[i]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable4.tab') if (n > n25) { a<-table.start() a<-table.row.start(a) a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'p-values',header=TRUE) a<-table.element(a,'Alternative Hypothesis',3,header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'breakpoint index',header=TRUE) a<-table.element(a,'greater',header=TRUE) a<-table.element(a,'2-sided',header=TRUE) a<-table.element(a,'less',header=TRUE) a<-table.row.end(a) for (mypoint in kp3:nmkm3) { a<-table.row.start(a) a<-table.element(a,mypoint,header=TRUE) a<-table.element(a,gqarr[mypoint-kp3+1,1]) a<-table.element(a,gqarr[mypoint-kp3+1,2]) a<-table.element(a,gqarr[mypoint-kp3+1,3]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable5.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Description',header=TRUE) a<-table.element(a,'# significant tests',header=TRUE) a<-table.element(a,'% significant tests',header=TRUE) a<-table.element(a,'OK/NOK',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'1% type I error level',header=TRUE) a<-table.element(a,numsignificant1) a<-table.element(a,numsignificant1/numgqtests) if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'5% type I error level',header=TRUE) a<-table.element(a,numsignificant5) a<-table.element(a,numsignificant5/numgqtests) if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'10% type I error level',header=TRUE) a<-table.element(a,numsignificant10) a<-table.element(a,numsignificant10/numgqtests) if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable6.tab') }

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